Surface and size effect of adxy-state superconductor

We study a ${\mathit{d}}_{\mathit{x}\mathit{y}}$-state superconducting film with specularly reflecting surfaces parallel to the y-z plane. The self-consistent pair potential and the surface density of states are calculated in the clean limit by use of the quasiclassical Green’s-function method within weak-coupling theory. The surface states have midgap states with energies around ω=0 as was pointed out by Hu [Phys. Rev. Lett. 72, 1526 (1994)]. We discuss the size dependence of the transition temperature.